Mathematics

Mathematics

Problem

Consider the system written in mixed order of variables: 2y − 3 = 5x, 4 = z − x + 2y, y + 6 = 3x − 2z. With variables arranged in the order (x, y, z), which of the following represents the correct matrix equation AX = B? a) (520−12−131−2) ⁣(xyz)=(−346)\begin{pmatrix}5 & 2 & 0 \\ -1 & 2 & -1 \\ 3 & 1 & -2\end{pmatrix}\!\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}-3\\4\\6\end{pmatrix} b) (5−20−1213−1−2) ⁣(xyz)=(−346)\begin{pmatrix}5 & -2 & 0 \\ -1 & 2 & 1 \\ 3 & -1 & -2\end{pmatrix}\!\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}-3\\4\\6\end{pmatrix} c) (−5201−2−1−312) ⁣(xyz)=(34−6)\begin{pmatrix}-5 & 2 & 0 \\ 1 & -2 & -1 \\ -3 & 1 & 2\end{pmatrix}\!\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}3\\4\\-6\end{pmatrix} d) (5−20−1213−1−2) ⁣(xyz)=(3−46)\begin{pmatrix}5 & -2 & 0 \\ -1 & 2 & 1 \\ 3 & -1 & -2\end{pmatrix}\!\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}3\\-4\\6\end{pmatrix}

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